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A100575
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Half the number of permutations of 0..n with exactly two maxima.
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9
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0, 0, 1, 8, 44, 208, 912, 3840, 15808, 64256, 259328, 1042432, 4180992, 16748544, 67047424, 268304384, 1073463296, 4294377472, 17178624000, 68716855296, 274872401920, 1099500093440, 4398022393856, 17592135712768, 70368639320064
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OFFSET
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0,4
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COMMENTS
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Coefficient of the e^(2x) term in the numerator of the n-th derivative of 1/(2-e^x).
This sequence, multiplied by 8, appears in a combinatorial problem about DNA chips. - Bruno Petazzoni (bruno(AT)enix.org), Apr 18 2007
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LINKS
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FORMULA
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G.f.: x^2/((1-2*x)^2*(1-4*x)).
a(n) = Sum_{k=0..n} (-1)^k*3^(n-k)*binomial(n, k)*floor(k/2). (End)
a(n) = 4^(n-1) - (n+1)*2^(n-2). - Bruno Petazzoni (bruno(AT)enix.org), Apr 18 2007
E.g.f.: (1/4)*(exp(4*x) - (1 + 2*x)*exp(2*x)). - G. C. Greubel, Mar 21 2022
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EXAMPLE
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a(2)=1 because there are two maxima in 2,0,1 and 1,0,2
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MATHEMATICA
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d = Drop[ Flatten[ CoefficientList[ Table[ Simplify[ D[1/(2 - E^x), {x, n}]*(E^x - 2)^(n + 1)/E^x], {n, 2, 24}], E^x]], 1]; a = {}; Do[AppendTo[a, Abs[d[[n(n + 1)/2]]]], {n, 23}]; a (* Robert G. Wilson v, Dec 01 2004 *)
LinearRecurrence[{8, -20, 16}, {0, 0, 1}, 30] (* Harvey P. Dale, Apr 21 2020 *)
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PROG
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(Sage) [2^(n-2)*(2^n -(n+1)) for n in (0..30)] # G. C. Greubel, Mar 21 2022
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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Definition corrected by Bruno Petazzoni (bruno(AT)enix.org), Apr 13 2007
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STATUS
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approved
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